Asymmetric conjugate priors for large Bayesian VARs

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior this setting is the natural conjugate as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at expense modeling flexibility, rules out cross?variable shrinkage, that shrinking coefficients on lags other variables more aggressively than those own lags. We develop has best both worlds: can accommodate while maintaining many results, such closed?form expression marginal likelihood. new also fast simulation—for BVAR with 100 4 lags, obtaining 10,000 draws takes less half minute standard desktop. demonstrate usefulness via structural analysis using 15?variable VAR sign restrictions identify 5 shocks.